In the number series 4, 16, 36, 64, the next term is _______. – UGC NET Question

The terms are squares of consecutive even numbers: 2² = 4, 4² = 16, 6² = 36 and 8² = 64. The next even number in sequence is 10. Squaring 10 gives 100. Therefore, 100 is the next term that preserves this structure.

Option A:
Option A is 90, which is not a perfect square and cannot be written as k² for an integer k. It breaks the pattern of exact squares. Hence, this option is not suitable.

Option B:
Option B is 96, again not a perfect square of an integer. There is no clear way to match it with the rule based on even squares. Therefore, 96 is not correct.

Option C:
Option C equals 100, which is 10² and follows 2², 4², 6² and 8² naturally. The extended series 4, 16, 36, 64, 100 completes the pattern of consecutive even squares. This makes 100 the valid continuation.

Option D:
Option D is 108, which lies between 10² and 11² but is not itself a square. Since the rule is precisely about squares, 108 cannot be accepted.